1. Field
The current invention relates to quality assurance. More particularly, the present invention relates to a method and apparatus for waveform quality measurement.
2. Background
Recently, communication systems have been developed to allow transmission of signals from an origination station to a physically distinct destination station. In transmitting signals from the origination station over a communication link, the signal is first converted into a form suitable for efficient transmission over the communication link. As used herein, the communication link comprises a medium over which a signal is transmitted. Conversion, or modulation, of the signal involves varying a parameter of a carrier wave in accordance with the signal in such a way that the spectrum of the resulting modulated carrier is confined within the communication link bandwidth. At the destination station the original signal is replicated from a version of the modulated carrier received over the communication link. Such a replication is generally achieved by using an inverse of the modulation process employed by the origination station.
Modulation also facilitates multiple-access, i.e., simultaneous transmission and/or reception, of several signals over a common communication link. Multiple-access communication systems often include a plurality of remote subscriber units requiring intermittent service of relatively short duration rather than continuous access to the common communication link. Several multiple-access techniques are known in the art, such as time division multiple-access (TDMA), frequency division multiple-access (FDMA), and amplitude modulation (AM). Another type of a multiple-access technique is a code division multiple-access (CDMA) spread spectrum system that conforms to the “TIA/EIA/IS-95 Mobile Station-Base Station Compatibility Standard for Dual-Mode Wide-Band Spread Spectrum Cellular System,” hereinafter referred to as the IS-95 standard. The use of CDMA techniques in a multiple-access communication system is disclosed in U.S. Pat. No. 4,901,307, entitled “SPREAD SPECTRUM MULTIPLE-ACCESS COMMUNICATION SYSTEM USING SATELLITE OR TERRESTRIAL REPEATERS,” and U.S. Pat. No. 5,103,459, entitled “SYSTEM AND METHOD FOR GENERATING SIGNAL WAVEFORMS IN A CDMA CELLULAR TELEPHONE SYSTEM,” both assigned to the assignee of the present invention and incorporated herein by reference.
FIG. 1 illustrates an ideal waveform 100 of an embodiment of a code division communication system in accordance with the IS-95 standard. For the purposes of this document, a waveform is a manifestation, representation or visualization of a wave, pulse or transition. The idealized waveform 100 comprises parallel channels 102 distinguished from one another by a cover code. The cover code in a communication system according to the IS-95 standard comprises Walsh codes. The ideal waveform 100 is then quadrature spreaded, baseband filtered and upconverted on a carrier frequency. The resulting modulated waveform 100, is expressed as:
                              s          ⁡                      (            t            )                          =                              ∑            i                    ⁢                                                    R                i                            ⁡                              (                t                )                                      ⁢                          ⅇ                                                -                  j                                ⁢                                                                  ⁢                                  ω                  c                                ⁢                t                                                                        (        1        )            where:
ωc is the nominal carrier frequency of the waveform;
i is the index of the code channels summation; and
Ri(t) is the complex envelope of the ideal i-th code channel.
Equipment, e.g., a transmitter of the code division communication system, generates actual waveform x(t) that is different from the ideal waveform. Such an actual waveform x(t) is expressed as:
                              x          ⁡                      (            t            )                          =                              ∑            i                    ⁢                                                    b                i                            [                                                                    R                    i                                    ⁡                                      (                                          t                      +                                              τ                        i                                                              )                                                  +                                                      E                    i                                    ⁡                                      (                    t                    )                                                              ]                        ·                          ⅇ                              -                                  j                  ⁡                                      [                                                                                            (                                                                                    ω                              c                                                        +                                                          Δ                              ⁢                                                                                                                          ⁢                              ω                                                                                )                                                ⁢                                                  (                                                      t                            +                                                          τ                              i                                                                                )                                                                    +                                              θ                        i                                                              ]                                                                                                          (        2        )            where:
bi is the amplitude of the ideal waveform relative to the ideal waveform for the ith code channel;
τi is the time offset of the ideal waveform relative to the ideal waveform for the ith code channel;
Δωis the radian frequency offset of the signal;
θi is the phase offset of the ideal waveform relative to the ideal waveform for the ith code channel; and
Ei(t) is the complex envelope of the error (deviation from ideal) of the actual transmit signal for the i-th code channel.
The difference between the ideal waveform s(t) and the actual waveform x(t) is measured in terms of frequency tolerance, pilot time tolerance, and waveform compatibility. One method to perform such a measurement is to determine modulation accuracy defined as a fraction of power of the actual waveform x(t) that correlates with the ideal waveform s(t), when the transmitter is modulated by the code channels. The modulation accuracy is expressed as:
                              ρ          overall                =                                            ∫                              T                1                                            T                2                                      ⁢                                                                                                s                    ⁡                                          (                      t                      )                                                        ·                                                            x                      ⁡                                              (                        t                        )                                                              *                                                                              ·                              ⅆ                t                                                                        {                                                ∫                                      T                    1                                                        T                    2                                                  ⁢                                                                                                                          s                        ⁡                                                  (                          t                          )                                                                                                            2                                    ·                                      ⅆ                    t                                                              }                        ·                          {                                                ∫                  T                                      T                    2                                                  ⁢                                                                                                                          x                        ⁡                                                  (                          t                          )                                                                                                            2                                    ·                                      ⅆ                    t                                                              }                                                          (        3        )            where:
T1 is beginning of the integration period; and
T2 is the end of the integration period.
For discrete time systems, where s(t) and x(t) are sampled at ideal sampling points tk, Equation 3 can be written as:
                              ρ          overall                =                                            ∑                              k                =                1                            N                        ⁢                                                                                                S                    k                                    ·                                      X                    k                    *                                                                              2                                                          {                                                ∑                                      k                    =                    1                                    N                                ⁢                                                                                                S                      k                                                                            2                                            }                        ·                          {                                                ∑                                      k                    =                    1                                    N                                ⁢                                                                                                X                      k                                                                            2                                            }                                                          (        4        )            where:
Xk=x[k]=x(tk) is kth sample of the actual waveform; and
Sk=s[k]=s(tk) is the corresponding kth sample of the ideal waveform.
A multiple-access communication system may carry voice and/or data. An example of a communication system carrying both voice and data is a system in accordance with the IS-95 standard, which specifies transmitting voice and data over the communication link. A method for transmitting data in code channel frames of fixed size is described in detail in U.S. Pat. No. 5,504,773, entitled “METHOD AND APPARATUS FOR THE FORMATTING OF DATA FOR TRANSMISSION,” assigned to the assignee of the present invention and incorporated by reference herein. In accordance with the IS-95 standard, the data or voice is partitioned into code channel frames that are 20 milliseconds wide with data rates as high as 14.4 Kbps. Additional examples of communication systems carrying both voice and data comprise communication systems conforming to the “3rd Generation Partnership Project” (3GPP), embodied in a set of documents including Document Nos. 3G TS 25.211, 3G TS 25.212, 3G TS 25.213, and 3G TS 25.214 (the W-CDMA standard), or “TR-45.5 Physical Layer Standard for cdma2000 Spread Spectrum Systems” (the IS-2000 standard). Such communication systems use a waveform similar to the one discussed above.
Recently, a data only communication system for a high data rate (HDR) transmission has been developed. Such a communication system has been disclosed in co-pending application Ser. No. 08/963,386, entitled “METHOD and apparatus FOR HIGH RATE PACKET DATA transmission,” filed Nov. 3, 1997, now U.S. Pat. No. 6,574,211B2, issued on Jun. 3, 2003, assigned to the assignee of the present invention and incorporated by reference herein. The HDR communication system defines a set of data rates, ranging from 38.4 kbps to 2.4 Mbps, at which an origination terminal (access point, AP) may send data packets to a receiving terminal (access terminal, AT). The HDR system utilizes a waveform with channels distinguished both in time domain and code domain.
FIG. 2 illustrates such a waveform 200, modeled after a forward link waveform of the above-mentioned HDR system. The waveform 200 is defined in terms of frames 202. (Only frames 202a, 202b, and 202c are shown in FIG. 2.) In an exemplary embodiment, a frame comprises 16 time slots 204, each time slot 204 being 2048 chips long, corresponding to a 1.67 millisecond slot duration, and, consequently, a 26.67 ms frame duration. Each slot 204 is divided into two half-slots 204a and 204b, with pilot bursts 206a and 206b transmitted within each half-slot 204a and 204b. In an exemplary embodiment, each pilot burst 206a and 206b is 96 chips long, and is centered at the mid-point of its associated half-slot 204a and 204b. The pilot bursts 206a and 206b comprise a pilot channel signal covered by a Walsh cover with index 0. The pilot channel is used for synchronization purposes. A forward medium access control channel (MAC) 208 forms two bursts 208a and two bursts 208b of a length of 64 chips each. The MAC bursts 208a and 208b are transmitted immediately before and immediately after the pilot bursts 206a and 206b of each slot 204. In an exemplary embodiment, the MAC is composed of up to 63 code channels, which are orthogonally covered by 64-ary Walsh codes. Each code channel is identified by a MAC index, which has a value between 0 and 63 and identifies the unique 64-ary Walsh cover. The MAC indexes 0 and 1 are reserved. A reverse power control channel (RPC) is used to regulate the power of the reverse link signals for each subscriber station. The RPC is assigned to one of the available MACs with MAC index 5-63. The MAC with MAC index 4 is used for a reverse activity channel (RA), which performs flow control on a reverse traffic channel. The forward link traffic channel and control channel payload is sent in the remaining portions 210a of the first half-slot 204a and the remaining portions 210b of the second half-slot 204b. The forward traffic channel and control channel data are encoded, scrambled, and interleaved. The interleaved data are modulated, repeated, and punctured, as necessary. Then, the resulting sequences of modulation symbols are demultiplexed to form 16 pairs (in-phase and quadrature) of parallel streams. Each of the parallel streams is covered with a distinct 16-ary Walsh cover, yielding a code-distinguished channel 212.
The ideal waveform 200 is then quadrature spreaded, baseband-filtered and upconverted on a carrier frequency. The resulting modulated waveform 200, is expressed as:
                              s          ⁡                      (            t            )                          =                              ∑                          i              ⁡                              (                t                )                                              ⁢                                                    R                i                            ⁡                              (                t                )                                      ⁢                                                  ⁢                          ⅇ                                                -                  j                                ⁢                                                                  ⁢                                  ω                  c                                ⁢                t                                                                        (        5        )            where:
ωc is the nominal carrier frequency of the waveform;
i(t) is the index of the code channels. The index is time dependent as the number of code channels varies with time; and
Ri(t) is the complex envelope of the ideal i-th code channel, given as:
                                          R            i                    ⁡                      (            t            )                          =                              a            i                    [                                                    ∑                k                            ⁢                                                g                  ⁡                                      (                                          t                      -                                              kT                        c                                                              )                                                  ⁢                                  cos                  ⁡                                      (                                          ϕ                                              i                        ,                        k                                                              )                                                                        +                          j              ⁢                                                ∑                  k                                ⁢                                                      g                    ⁡                                          (                                              t                        -                                                  kT                          c                                                                    )                                                        ⁢                                      sin                    ⁡                                          (                                              ϕ                                                  i                          ,                          k                                                                    )                                                                                                    ]                                    (        6        )            where:
ai is the amplitude of the ith code channel;
g(t) is the unit impulse response of the baseband transmit filter;
φi,k is the phase of the kth chip for the ith code channel, occurring at discrete time tk=kTc.
Tc is a chip duration.
The transmitter of the HDR communication system generates an actual waveform x(t), given as:
                              x          ⁡                      (            t            )                          =                              ∑                          i              ⁡                              (                t                )                                              ⁢                                                    b                i                            [                                                                    R                    i                                    ⁡                                      (                                          t                      +                                              τ                        i                                                              )                                                  +                                                      E                    i                                    ⁡                                      (                    t                    )                                                              ]                        ·                          ⅇ                              -                                  j                  ⁢                                                                          [                                                                                    (                                                                              ω                            c                                                    +                                                      Δ                            ⁢                                                                                                                  ⁢                            ω                                                                          )                                            ⁢                                              (                                                  t                          +                                                      τ                            i                                                                          )                                                              +                                          θ                      i                                                        ]                                                                                        (        7        )            where
bi is the amplitude of the ideal waveform relative to the ideal waveform for the ith code channel;
τi is the time offset of the ideal waveform relative to the ideal waveform for the ith code channel;
Δω is the radian frequency offset of the signal;
θi is the phase offset of the ideal waveform relative to the ideal waveform for the ith code channel; and
Ei(t) is the complex envelope of the error (deviation from ideal) of the actual transmit signal for the i-th code channel.
Based on the complex time domain and code domain channelization of the waveform 200, the waveform quality measurement methods based on code domain channelization are inapplicable. Consequently, there is a need in the art for a method and an apparatus for a waveform quality measurement for waveforms channelized both in time domain and code domain.